LEACH (Low Energy Adaptive Clustering Hierarchy) [1] is one of the popular cluster-based structures, which has been widely proposed in wireless sensor networks. LEACH uses a TDMA based MAC protocol, and in order to maintain a balanced energy consumption, suggests that each node probabilistically become a cluster head. To reduce the energy consumption and to avoid the strict synchronization requirements of TDMA, we first apply a sleep-wakeup based decentralized MAC protocol to LEACH, then we present an analytic framework for obtaining the optimal probability with which a node becomes a cluster head in order to minimize the network’s energy consumption. The analysis is first presented for small networks, under the assumption of identical expected distance of all cluster heads from the sink. Then the analysis is extended for large networks to consider the case when the distances of various sections of the network from the sink may be different, since nodes further away have to spend ...